Question: Rewrite as a simplified fraction. ${2.48\overline{2} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2482.2222...\\ 100x &= 248.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2234}$ ${x = \dfrac{2234}{900}} $ ${x = \dfrac{1117}{450}} \text{or} {2 \dfrac{217}{450}}$